Nonlocality is today strongly associated with the idea of entanglement, but nonlocality is a property of a single quantum of light, whereas entanglement is a joint property of two quantum particles, depending on an even more subtle property called nonseparability.

Nonlocality is an essential element of the dual nature of light as both a wave and a particle (better sometimes a wave and sometimes a particle). We can visualize the wave function of quantum mechanics in the following way. The wave function is a probability amplitude whose squared modulus gives the probability of finding a particle in a particular (sic) location. As this function spreads out in space, we can think of it as a "possibilities function," showing all the locations in space where there is a non-zero probability of finding a particle. The power of quantum mechanics is that we can calculate the probability of finding the particle for each possibility.

When an electron is freely traveling (as opposed to an electron bound in an atom), or when a photon is emitted from an electron and is traveling though space, there are always many possible locations for an interaction. Therefore we can say that the "possibilities function" (or the more formal quantum wave function) is inherently and intuitively nonlocal!

Since Werner Heisenberg and Paul Dirac first discussed the "collapse" of the wave function (Dirac's projection postulate), it has been appropriate to say that "one of the many possibilities has been made actual." In the language of nonlocality, we can now even more clearly say that one of the nonlocal possibilities has been actualized or localized!

Scattering is better understood as the absorption and rapid re-emission of a photon, as pointed out by Einstein and Paul Ehrenfest in 1923, in response to an article by Wolfgang Pauli

In the case of the photon, it is localized when it has been scattered or absorbed by an electron. In the case of an electron, it might be a collision with another particle, or recombining with an ion to become bound in an atom. The electron is actually never found at a single point in four-dimensional space time, but remains nonlocal inside the minimal phase-space volume h3 required by the uncertainty principle (for example, a particular electron orbital wave function). Thus some physicists like to say there are no particles, just the appearance of a particle.

Albert Einstein was first to have seen single-particle nonlocality, in 1905, when he tried to understand how a spherical wave of light that goes off in many directions can be wholly absorbed at a single location. In his famous paper on the photo-electric effect (for which Einstein was awarded the Nobel Prize), he hypothesized that light must transmitted from one place to another as a discrete quantum of energy.

Einstein did not then use the term nonlocal or "local reality," but we can trace his thoughts backwards from 1935 to see that quantum nonlocality (and later nonseparability) were always major concerns, because neither can be made consistent with a continuous field theory and they may be inconsistent with the principle of relativity.

Einstein clearly described wave-particle duality as early as 1909, over a dozen years before the duality was made famous by Louis de Broglie's thesis showed that material particles also have a wavelike property.

When Einstein finished his great project of general relativity in 1916, he turned his attention back to light quanta and showed how electrons in atoms emit and absorb radiation. He found the process of emission was probabilistic (statistical). It is impossible to predict the time and the direction of the emission of a quantum of light, he said, just as Rutherford had shown the decay of a radioactive nucleus was statistical. The time and direction of an alpha particle ejected from a nucleus is pure chance.

Einstein said it was a "weakness" that the quantum theory was based on chance (Zufall in German). His 1916 work on the emission and absorption of light quanta (later called photons) predicted the amazing phenomenon of stimulated emission of radiation, which led to the development of the laser many decades later. As hard as it is to believe, most physicists, and especially Niels Bohr, refused to accept Einstein's theory of light quanta for another decade.

At the fifth Solvay conference in 1927, Einstein described his concern about nonlocality, but as we shall see, it appears he was not understood. Then, eight years later, Einstein made his strongest case against both nonlocality and nonseparability, with the famous 1935 Einstein-Podolsky-Rosen paradox paper. At last he was heard, but it brought little resolution to the problem of reconciling waves and particles. And it added the mystery of particles entangled in a two-particle wave function, which combines nonlocality and nonseparability, so that upon collapse the two particles appear in a spacelike separation with perfectly correlated properties, despite the inability to communicate instantaneously at that separation without violating the special theory of relativity.

Let's review Einstein's thinking on nonlocality, starting with his presentation at the fifth Solvay conference. Bohr and Heisenberg tell the story of Einstein at that conference repeatedly attempting to refute the uncertainty principle and perhaps restore deterministic physics. But the fragments that remain of what Einstein said on nonlocality indicate a much deeper criticism of quantum mechanics. Einstein's nonlocality remarks were not a formal presentation and were not reported in the conference proceedings. We know them only from brief notes on the general discussion and from what others said that Einstein said.

And here are the notes on Einstein's original remarks from the conference. They contain much of his 1935 EPR paper, except in 1927 only one particle is considered. Entanglement in EPR requires two identical particles.

MR ElNSTEIN. - Despite being conscious of the fact that I have not entered
deeply enough into the essence of quantum mechanics, nevertheless I want to
present here some general remarks.

One can take two positions towards the theory with respect to its postulated
domain of validity, which I wish to characterise with the aid of a simple example.

Let S be a screen provided with a small opening O (Fig. 2), and P a hemispherical
photographic film of large radius. Electrons impinge on S in the direction of the arrows. Some of these go through O, and because of the smallness of O and the speed of the particles, are dispersed uniformly over the directions of the hemisphere, and act on the film.

Both ways of conceiving the theory now have the following in common. There are de Broglie waves, which impinge approximately normally on S and are diffracted at O. Behind S there are spherical waves, which reach the screen P and
whose intensity at P is responsible [massgebend] for what happens at P.

We can now characterise the two points of view as follows.

The waves give the probability or possibilities for a single electron being found at different locations in an ensemble of identical experiments. A wave does not describe a cloud of electrons as Schrödinger had hoped.

1. Conception I. - The de Broglie-Schrödinger waves do not correspond to a single electron, but to a cloud of electrons extended in space. The theory gives no information about individual processes, but only about the ensemble of an infinity of elementary processes.

The theory is not complete in this sense. It is a theory that makes probabilistic predictions that are confirmed perfectly by the statistics of many experiments.

2. Conception II. - The theory claims to be a complete theory of individual processes. Each particle directed towards the screen, as far as can be determined by its position and speed, is described by a packet of de Broglie-Schrödinger waves of short wavelength and small angular width. This wave packet is diffracted and, after diffraction, partly reaches the film P in a state of resolution [un etat de resolution].

According to the first, purely statistical, point of view | ψ |2 expresses the
probability that there exists at the point considered a particular particle of the cloud, for example at a given point on the screen.

By the same particle, Einstein means that the one individual particle has a possibility of being found at more than one (indeed many) locations on the screen. This is so.

According to the second, | ψ |2 expresses the probability that at a given instant
the same particle is present at a given point (for example on the screen). Here,
the theory refers to an individual process and claims to describe everything that is governed by laws.

The second conception goes further than the first, in the sense that all the
information resulting from I results also from the theory by virtue of II, but
the converse is not true. It is only by virtue of II that the theory contains the
consequence that the conservation laws are valid for the elementary process; it is only from II that the theory can derive the result of the experiment of Geiger and Bothe, and can explain the fact that in the Wilson [cloud] chamber the droplets stemming from an α-particle are situated very nearly on continuous lines.

Einstein is right that the one elementary process has a possibility of action elsewhere, but that could not mean producing an actual second particle. That would contradict conservation laws.

The "mechanism" of action-at-a-distance is simply the disappearance of possibilities elsewhere when a particle is actualized (localized) somewhere

But on the other hand, I have objections to make to conception II. The scattered
wave directed towards P does not show any privileged direction. If | ψ |2 were
simply regarded as the probability that at a certain point a given particle is found at
a given time, it could happen that the same elementary process produces an action in two or several places on the screen. But the interpretation, according to which | ψ |2 expresses the probability that this particle is found at a given point, assumes an entirely peculiar mechanism of action at a distance, which prevents the wave continuously distributed in space from producing an action in two places on the
screen.

When a particle appears - just one of the multiple nonlocal possibilities becomes actual or localized - at a specific point P , what becomes of the wave that was going off to in all other directions? Its "collapse" - the instantaneous going to zero of probabilities - appears to Einstein to violate his relativity principle.

In my opinion, one can remove this objection only in the following way, that one
does not describe the process solely by the Schrödinger wave, but that at the same
time one localises the particle during the propagation. I think that Mr de Broglie is
right to search in this direction. If one works solely with the Schrödinger waves,
interpretation II of | ψ |2 implies to my mind a contradiction with the postulate of relativity.

The permutation of two identical particles does not produce two different points in multidimensional (configuration space). For example, interchange of the two electrons in the filled first electron shell, 1s2, just produces a change of sign for the two-particle wave function.

I should also like to point out briefly two arguments which seem to me to speak against the point of view II. This [view] is essentially tied to a multi-dimensional representation (configuration space), since only this mode of representation makes
possible the interpretation of | ψ |2 peculiar to conception II. Now, it seems to me
that objections of principle are opposed to this multi-dimensional representation.
In this representation, indeed, two configurations of a system that are distinguished only by the permutation of two particles of the same species are represented by two different points (in configuration space), which is not in accord with the new results in statistics. Furthermore, the feature of forces of acting only at small spatial distances finds a less natural expression in configuration space than in the space of three or four dimensions.

Bohr's reaction to Einstein's presentation has been preserved. He didn't understand a word! He disingenuously claims he does not know what quantum mechanics is. His response is vague and ends with his vague ideas on complementarity and the inability to describe a causal spacetime reality.

Does Bohr really not understand? Einstein has been making this general point for many years. Only recently has Bohr taken Einstein's concept of light quanta seriously.

MR BOHR. I feel myself in a very difficult position because I don't understand what precisely is the point which Einstein wants to [make]. No doubt it is my fault.

As regards general problem I feel its difficulties. I would put [the] problem in [an]other way. I do not know what quantum mechanics is. I think we are dealing with some mathematical methods which are adequate for description of our experiments Using a rigorous wave theory we are claiming something which the theory cannot possibly give. [We must realise] that we are away from that state where we could hope of describing things on classical theories. [I] Understand [the] same view is held by Born and Heisenberg. I think that we actually just try to meet, as in all other theories, some requirements of nature, but [the} difficulty is that we must use words which remind [us] of older theories. The whole foundation for causal spacetime description is taken away by quantum theory, for it is based on [the] assumption of observations without interference. ... excluding interference means exclusion of experiment and the whole meaning of space and time observation ... because we [have] interaction [between object and measuring instrument] and thereby we put us on a quite different standpoint than we thought we could take in classical theories. If we speak of observations we play with a statistical problem There are certain features complementary to the wave pictures (existence of individuals). ...

The saying that spacetime is an abstraction might seem a philosophical triviality but nature reminds us that we are dealing with something of practical interest. Depends on how I consider theory. I may not have understood, but I think the whole thing lies [therein that the] theory is nothing else [but] a tool for meeting our requirements and I think it does.

Twenty-two years later, in his contribution to the Schilpp memorial volume on Einstein, Bohr had no better response to Einstein's 1927 concerns. But he does remember and provides a picture of what Einstein drew on the blackboard.

Here is Bohr's 1949 recollection:

At the general discussion in Como, we all missed the presence of Einstein,
but soon after, in October 1927, I had the opportunity to meet him in Brussels
at the Fifth Physical Conference of the Solvay Institute, which was devoted
to the theme "Electrons and Photons."

Note that they wanted Einstein's reaction to their work, but actually took little interest in Einstein's concern about the nonlocal implications of quantum mechanics.

At the Solvay meetings,
Einstein had from their beginning been a most prominent figure, and several
of us came to the conference with great anticipations to learn his reaction
to the latest stage of the development which, to our view, went far in
clarifying the problems which he had himself from the outset elicited so
ingeniously. During the discussions, where the whole subject was reviewed
by contributions from many sides and where also the arguments mentioned
in the preceding pages were again presented, Einstein expressed, however,
a deep concern over the extent to which a causal account in space and time
was abandoned in quantum mechanics.

To illustrate his attitude, Einstein referred at one of the sessions
to the simple example, illustrated by Fig. 1, of a particle (electron or
photon) penetrating through a hole or a narrow slit in a diaphragm placed
at some distance before a photographic plate.

On account of the diffraction of the wave connected with the motion
of the particle and indicated in the figure by the thin lines, it is under
such conditions not possible to predict with certainty at what point the
electron will arrive at the photographic plate, but only to calculate the
probability that, in an experiment, the electron will be found within any
given region of the plate.

The "nonlocal" effects at point B are just the probability of an electron being found at point B goes to zero instantly (as if an action at a distance) when an electron is localized at point A

The apparent difficulty, in this description,
which Einstein felt so acutely, is the fact that, if in the experiment
the electron is recorded at one point A of the plate, then it is out of
the question of ever observing an effect of this electron at another point
(B), although the laws of ordinary wave propagation offer no room for a
correlation between two such events.

Although Bohr seems to have missed Einstein's point completely, Werner Heisenberg at least came to understand it very well. In his 1930 lectures at the University of Chicago, Heisenberg presented a critique of both particle and wave pictures, including a new example of nonlocality that Einstein had apparently developed since 1927. He wrote:

In relation to these considerations, one other idealized experiment (due to Einstein) may be considered. We imagine a photon which is represented by a wave packet built up out of Maxwell waves. It will thus have a certain spatial extension and also a certain range of frequency. By reflection at a semi-transparent mirror, it is possible to decompose it into two parts, a reflected and a transmitted packet. There is then a definite probability for finding the photon either in one part or in the other part of the divided wave packet. After a sufficient time the two parts will be separated by any distance desired; now if an experiment yields the result that the photon is, say, in the reflected part of the packet, then the probability of finding the photon in the other part of the packet immediately becomes zero. The experiment at the position of the reflected packet thus exerts a kind of action (reduction of the wave packet) at the distant point occupied by the transmitted packet, and one sees that this action is propagated with a velocity greater than that of light. However, it is also obvious that this kind of action can never be utilized for the transmission of signals so that it is not in conflict with the postulates of the theory of relativity.

Working backwards in time to Einstein's 1905 insight into nonlocality, we now review his amazing arguments about wave-particle duality in 1909.

Einstein greatly expanded his light-quantum hypothesis in a presentation at the Salzburg conference in September, 1909. He argued that the interaction of radiation and matter involved elementary processes that are not reversible, a deep insight into the irreversibility of natural processes. While incoming spherical waves of radiation are mathematically possible, they are not practically achievable. Nature appears to be asymmetric in time. He speculates that the continuous electromagnetic field might be made up of large numbers of light quanta - singular points in the field that superimpose to create the wavelike behavior.

Although he could not formulate a mathematical theory that does justice to both the oscillatory and quantum structures - the wave and particle pictures, Einstein argued that they are compatible. This was almost fifteen years before wave mechanics and quantum mechanics. And because gases behave statistically, he knows that the connection between wave and particles may involve probabilistic behavior, which he will prove in 1916. Here he is in 1909:

When light was shown to exhibit interference and diffraction, it seemed almost certain that light should be considered a wave.

The greatest advance in theoretical optics since the introduction of the oscillation theory was Maxwell's brilliant discovery that light can be understood as an electromagnetic process...One became used to treating electric and magnetic fields as fundamental concepts that did not require a mechanical interpretation.

This path leads to the so-called relativity theory. I only wish to bring in one of its consequences, for it brings with it certain modifications of the fundamental ideas of physics. It turns out that the inertial mass of an object decreases by L / c2 when that object emits radiation of energy L...the inertial mass of an object is diminished by the emission of light.

Now Einstein looks for symmetry and equivalent treatment for interchangeable matter and energy.

The energy given up was part of the mass of the object. One can further conclude that every absorption or release of energy brings with it an increase or decrease in the mass of the object under consideration. Energy and mass seem to be just as equivalent as heat and mechanical energy.

Relativity theory has changed our views on light. Light is conceived not as a manifestation of the state of some hypothetical medium, but rather as an independent entity like matter. Moreover, this theory shares with the corpuscular theory of light the unusual property that light carries inertial mass from the emitting to the absorbing object. Relativity theory does not alter our conception of radiation's structure; in particular, it does not affect the distribution of energy in radiation-filled space.

Einstein is about to tell us that the distribution of energy in radiation-filled space may be similar in some respects to the distribution of particles in matter-filled space!

Nevertheless, with respect to this question, I believe that we stand at the beginning of a development of the greatest importance that cannot yet be surveyed. The statements that follow are largely my personal opinion, or the results of considerations that have not yet been checked enough by others. If I present them here in spite of their uncertainty, the reason is not an excessive faith in my own views, but rather the hope to induce one or another of you to deal with the questions considered.

In the kinetic theory of molecules, for every process in which only a few elementary particles participate (e.g., molecular collisions), the inverse process also exists. But that is not the case for the elementary processes of radiation.

Incoming spherical waves (the advanced potential considered by Wheeler and Feynman in 1945) are never observed in nature. Radiation is irreversible, one of the arrows of time

According to our prevailing theory, an oscillating ion generates a spherical wave that propagates outwards. The inverse process does not exist as an elementary process. A converging spherical wave is mathematically possible, to be sure; but to approach its realization requires a vast number of emitting entities. The elementary process of emission is not invertible. In this, I believe, our oscillation theory does not hit the mark. Newton's emission theory of light seems to contain more truth with respect to this point than the oscillation theory since, first of all, the energy given to a light particle is not scattered over infinite space, but remains available for an elementary process of absorption.

Consider the laws governing the production of secondary cathode radiation by X-rays. If primary cathode rays impinge on a metal plate P1, they produce X-rays. If these X-rays impinge on a second metal plate P2, cathode rays are again produced whose speed is of the same order as that of the primary cathode rays.

As far as we know today, the speed of the secondary cathode rays depends neither on the distance between P1 and P2, nor on the intensity of the primary cathode rays, but rather entirely on the speed of the primary cathode rays. Let's assume that this is strictly true. What would happen if we reduced the intensity of the primary cathode rays or the size of P1 on which they fall, so that the impact of an electron of the primary cathode rays can be considered an isolated process?

In his remarks after the talk, Johannes Stark confirmed that he had observed a single X-ray that traveled as far as ten meters and ejected a similar energy electron from P2.

If the above is really true then, because of the independence of the secondary cathode rays' speed on the primary cathode rays' intensity, we must assume that an electron impinging on P1 will either cause no electrons to be produced at P2, or else a secondary emission of an electron whose speed is of the same order as that of the initial electron impinging on P1. In other words, the elementary process of radiation seems to occur in such a way that it does not scatter the energy of the primary electron in a spherical wave propagating in every direction, as the oscillation theory demands.

That energy is possibly available "somewhere else" is the key idea of nonlocality that Einstein will present in 1927 at the Solvay conference

Rather, at least a large part of this energy seems to be available at some place on P2, or somewhere else. The elementary process of the emission of radiation appears to be directional. Moreover, one has the impression that the production of X-rays at P1 and the production of secondary cathode rays at P2 are essentially inverse processes.

Therefore, the constitution of radiation seems to be different from what our oscillation theory predicts. The theory of thermal radiation has given important clues about this, mostly by the theory on which Planck based his radiation formula...

Four years before the Bohr atom, Einstein imagines a radiative resonator (an atom) that can only emit or absorb his light quanta in units of hν.

Planck's "monstrous assumption" is that the resonator/atoms could only have energy states as multiples of hν. We can ask why Bohr didn't refer to these similar ideas. Instead, Bohr refused to accept light quanta (photons) well into the 1920's

Planck's theory leads to the following conjecture. If it is really true that a radiative resonator can only assume energy values that are multiples of hν, the obvious assumption is that the emission and absorption of light occurs only in these energy quantities. On the basis of this hypothesis, the light-quanta hypothesis, the questions raised above about the emission and absorption of light can be answered. As far as we know, the quantitative consequences of this light-quanta hypothesis are confirmed. This provokes the following question. Is it not thinkable that Planck's radiation formula is correct, but that another derivation could be found that does not rest on such a seemingly monstrous assumption as Planck's theory? Is it not possible to replace the light-quanta hypothesis with another assumption, with which one could do justice to known phenomena? If it is necessary to modify the theory's elements, couldn't one keep the propagation laws intact, and only change the conceptions of the elementary processes of emission and absorption?

As far as I know, no mathematical theory has been advanced that does justice to both its oscillatory structure and its quantum structure...

Anyway, this conception seems to me the most natural: that the manifestation of light's electromagnetic waves is constrained at singularity points, like the manifestation of electrostatic fields in the theory of the electron. It cannot be ruled out that, in such a theory, the entire energy of the electromagnetic field could be viewed as localized in these singularities, just like the old theory of action-at-a-distance. I imagine to myself, each such singular point surrounded by a field that has essentially the same character as a plane wave, and whose amplitude decreases with the distance between the singular points. If many such singularities are separated by a distance small with respect to the dimensions of the field of one singular point, their fields will be superimposed, and will form in their totality an oscillating field that is only slightly different from the oscillating field in our present electromagnetic theory of light. Of course, it need not be emphasized that such a picture is worthless unless it leads to an exact theory. I only wished to illustrate that the two structural properties of radiation according to Planck's formula (oscillation structure and quantum structure) should not be considered incompatible with one another.

Now, back to 1905. Einstein's three 1905 papers on relativity, Brownian motion, and the light-quantum hypothesis (mischaracterized by many historians as the photo-electric effect), not only quantize the radiation field (Planck had only quantized matter, the virtual oscillators), but they also show on a careful reading that Einstein was concerned about faster-than-light actions thirty years before his Einstein-Podolsky-Rosen paper popularized the mysteries and paradoxes of quantum nonlocality and entanglement.

Despite his foundational work quantizing radiation, Einstein rarely gets any credit for his contributions. There are a number of important reasons for this, which lead historians of quantum theory to start with Planck's quantum of action, then jump over Einstein's 1905 papers and his 1909 work on wave-particle duality to Niels Bohr's "old quantum theory" of the atom in 1913. Today, Bohr's "quantum jump" of an electron between stationary states is described as emitting or absorbing a "photon" of energy hν. In actuality, Bohr fought against Einstein's light-quantum hypothesis until the mid-1920's.

Besides quantizing energy and seeing the interchangeability of radiation and matter, E = mc2, Einstein was the first scientist to see many of the most fundamental aspects of quantum physics, e.g., nonlocality and instantaneous action-at-a-distance (1905), wave-particle duality (1909), statistical elementary processes that introduce indeterminism and acausality whenever matter and radiation interact (1916-17), coherence, interference, and the indistinguishability of elementary particles (1925), and the nonseparability and entanglement of interacting particles (1935).

Ironically, and even tragically, Einstein could never accept most of his quantum discoveries, because they conflicted with his basic idea that nature is best described by a continuous field theory using differential equations that are functions of "local" variables, primarily the space-time four-vector of his general relativistic theory. Einstein's idea of a "local" reality is one where "action-at-a-distance" is limited to causal effects that propagate at or below the speed of light, according to his theory of relativity. He also famously disliked indeterminism ("God does not play dice").

Einstein's believed that quantum theory, as good as it is (and he saw nothing better), is "incomplete" because its statistical predictions (phenomenally accurate in the limit of large numbers of identical experiments - "ensembles" Einstein called them), tell us nothing about individual systems.

Even worse, he thought that the wave functions of entangled systems predict faster-than-light correlations of properties between events in a space-like separation, violating his theory of relativity. This was the heart of his famous EPR paradox paper in 1935 (which introduced the concept of nonseparability), but we shall now see that Einstein was already concerned about faster-than-light transfer of energy in his very first paper on quantum theory.

The light-quantum hypothesis (1905)

How can energy spread continuously over a large volume later be absorbed in its entirety, without contradicting his principle of relativity? Einstein sees this, but does not say so explicitly, as we saw above, until 1927.

The energy
of a ponderable body cannot be subdivided into
arbitrarily many or arbitrarily small parts, while
the energy of a beam of light from a point source
(according to the Maxwellian theory of light or,
more generally, according to any wave theory) is
continuously spread over an ever increasing
volume.

The wave theory of light, which operates with
continuous spatial functions, has worked well in
the representation of purely optical phenomena
and will probably never be replaced by another
theory. It should be kept in mind, however, that
the optical observations refer to time averages
rather than instantaneous values. In spite of the
complete experimental confirmation of the theory
as applied to diffraction, reflection, refraction,
dispersion, etc., it is still conceivable that the
theory of light which operates with continuous
spatial functions may lead to contradictions
with experience when it is applied to the phenomena of emission and transformation of light.

It seems to me that the observations associated
with blackbody radiation, fluorescence, the
production of cathode rays by ultraviolet light,
and other related phenomena connected with the
emission or transformation of light are more
readily understood if one assumes that the energy
of light is discontinuously distributed in space.

In particular, the photoelectric effect showed discontinuous discrete light quanta, though it was doubted until the Compton Effect in 1923.

In accordance with the assumption to be considered here, the energy of a light ray spreading
out from a point source is not continuously
distributed over an increasing space but consists
of a finite number of energy quanta which are
localized at points in space, which move without
dividing, and which can only be produced and
absorbed as complete units.

We therefore arrive at the conclusion: the
greater the energy density and the wavelength
of a radiation, the more useful do the theoretical
principles we have employed turn out to be; for
small wavelengths and small radiation densities,
however, these principles fail us completely.

Thermodynamically, radiation behaves like a gas. Light cannot be spread out continuously in all directions if the energy is absorbed as a unit that ejects a photo-electron in the photo-electric effect.

[W]e further conclude that: Monochromatic radiation of low density (within the
range of validity of Wien's radiation formula)
behaves thermodynamically as though it consisted of a number of independent energy quanta.

The usual conception, that the energy of light
is continuously distributed over the space
through which it propagates, encounters very
serious difficulties when one attempts to explain
the photoelectric phenomena,

Why did Bohr not see in 1913, or Einstein point out to him, that when an electron in an atom absorbs or emits energy, the jumping electron is accompanied by a single light quantum?

According to the concept that the incident
light consists of energy quanta..., however, one can conceive of the ejection
of electrons by light in the following way. Energy
quanta penetrate into the surface layer of the
body, and their energy is transformed, at least in
part, into kinetic energy of electrons. The simplest
way to imagine this is that a light quantum
delivers its entire energy to a single electron; we
shall assume that this is what happens.

We have shown that ever since Einstein hypothesized that light consists of small quanta of energy, he was concerned about a conflict with the picture of light as a wave. He saw that in many places distant from the point in space and time where the quantum actually appears as a detected particle, at that instant or a moment before, there existed the possibility (or probability) that the particle might have appeared somewhere else, somewhere separated in space so far as to prohibit signals from the detected quantum to that distant point where the particle did not appear.

How, he asked, or what sort of "action-at-a-distance" suppressed some sort of action happening at one of those other places where the probability of appearance had been non-zero? While Einstein is vague about the action that he has in mind, it is at least the disappearance, the sudden going to zero, of that probability. He cannot be imagining a second appearance of a particle. That would violate conservation of energy. He may be thinking of the interpretation of the wave function as representing some kind of knowledge about where the associated particle is likely to be found. How does that "knowledge" at the distant point or possible points "learn" that the particle will not in fact be appearing there?

Why does Einstein think that anything is needed beyond the fact that in this particular experiment, it appeared where it did and nowhere else?
something substantial = information
For Heisenberg - knowledge